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Chapter 3

Chapter 3. Dead Time Compensation – Smith Predictor, A Model Based Approach. 1. Effects of Dead-Time (Time Delay). Process with large dead time (relative to the time constant of the process) are difficult to control by pure feedback alone:

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Chapter 3

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  1. Chapter 3 Dead Time Compensation – Smith Predictor, A Model Based Approach

  2. 1. Effects of Dead-Time (Time Delay) • Process with large dead time (relative to the time constant of the process) are difficult to control by pure feedback alone: • Effect of disturbances is not seen by controller for a while • Effect of control action is not seen at the output for a while. This causes controller to take additional compensation unnecessary • This results in a loop that has inherently built in limitations to control

  3. Example – A Bode Plot Example h=tf(1,[1 3 3 1],'inputdelay',1);

  4. Example- continued, case without time delay

  5. PID Control Results- Case with delay (Kc=1,Ki=1,Kd=1)

  6. PID Control Results- Case without delay (Kc=1,Ki=1,Kd=1)

  7. 2. Causes of Dead-Time • Transportation lag (long pipelines) • Sampling downstream of the process • Slow measuring device: GC • Large number of first-order time constants in series (e.g. distillation column) • Sampling delays introduced by computer control

  8. Process Controller ＋ － Controller mechanism Process Controller ＋ － Dead-time compensator ＋ ＋ Process Controller ＋ － 3. The Smith Predictor

  9. Control with Smith Predictor: (Kc=1,Ki=1,Kd=1)

  10. d ＋ ＋ － － ＋ － d Alternate form

  11. Example 2: Long time delay 1 G(s)= exp(-3*s) * --------------------- s^3 + 3 s^2 + 3 s + 1 Mag=-3.3dB=20log10(AR); AR=0.6839; Wu=0.5;Pu=2π/0.5=12.5664 Ku=1/0.6839=1.4622 Kc=0.8601 Taui=Pu/2=6.2832 Taud=Pu/8=1.5708

  12. Load Disturbance Response

  13. Process Controller mechanism + Gc(s) G(s) e-tds - + (1-e-td’s)G’(s) - The Effect of Modeling Error Errors in td’,G’ both cause the control system to degrade

  14. Smith Predictor with Modeling Error Plant=e-s/(s3+3s2+3s+1) Model=e-s/(s3+s2+s+1) Model=e-0.5s/(s3+s2+s+1)

  15. Analytical Predictor y(s) GC(s) GPe-DS ySP Analytical Predictor y(t+D) Analytical Predictor is a model that projects what y will be D units into the future (on-line model identification)

  16. Step response to manipulate variable y(t) time Processes with inverse response The output goes to the wrong way first Example: This can occurs in (1) reboiler level response to change in heat input to the reboiler. (2) Some tubular reactor exist temperature To inlet flow rate . Inverse response is caused by a RHP zero

  17. Example: Inverse response of concentration and temperature to a chanbe in process flow of 0.15 ft3/min

  18. Process with inverse response Controller + + Gc(s) - -

  19. Process with inverse response Controller mechanism Controller + + Gc(s) - - + -

  20. Open Loop Response Analysis

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